Equivalent a Posteriori Error Estimator of Spectral Approximation for Control Problems with Integral Control-State Constraints in One Dimension
Year: 2016
Author: Fenglin Huang, Yanping Chen, Xiulian Shi
Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 3 : pp. 464–484
Abstract
In this paper, we investigate the Galerkin spectral approximation for elliptic control problems with integral control and state constraints. Firstly, an a posteriori error estimator is established, which can be acted as the equivalent indicator with explicit expression. Secondly, appropriate base functions of the discrete spaces make it probable to solve the discrete system. Numerical test indicates the reliability and efficiency of the estimator, and shows the proposed method is competitive for this class of control problems. These discussions can certainly be extended to two- and three-dimensional cases.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2014.m591
Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 3 : pp. 464–484
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Optimal control elliptic equations control-state constraints spectral method a posteriori error estimator.